Pricing American Options Under Stochastic Volatility and Stochastic Interest Rates PDF Download
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Author: Jannick B. G. Schreiner
Publisher:
ISBN:
Category :
Languages : en
Pages : 71
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Book Description
Author: Jannick B. G. Schreiner
Publisher:
ISBN:
Category :
Languages : en
Pages : 71
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Author: Alexey Medvedev
Publisher:
ISBN:
Category :
Languages : en
Pages : 48
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Author: Arun Chockalingam
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Book Description
The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrates that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes. Option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on European options. We consider the problem of pricing American options under stochastic volatility which has relatively had much less attention from literature. First, we develop an exercise-policy improvement procedure to compute the optimal exercise policy and option price. We show that the scheme monotonically converges for various popular stochastic volatility models in literature. Second, using this computational tool, we explore a variety of questions that seek insights into the dependence of option prices, exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility.
Author: Manisha Goswami
Publisher:
ISBN:
Category :
Languages : en
Pages :
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The approximate method to price American options makes use of the fact that accurate pricing of these options does not require exact determination of the early exercise boundary. Thus, the procedure mixes the two models of constant and stochastic volatility. The idea is to obtain early exercise boundary through constant volatility model using the approximation methods of AitSahlia and Lai or Ju and then utilize this boundary to price the options under stochastic volatility models. The data on S & P 100 Index American options is used to analyze the pricing performance of the mixing of the two models. The performance is studied with respect to percentage pricing error and absolute pricing errors for each money-ness maturity group.
Author: Marc Sáez
Publisher:
ISBN:
Category : Options (Finance)
Languages : en
Pages : 29
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Author: Suchandan Guha
Publisher:
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Category :
Languages : en
Pages :
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ABSTRACT: We developed two new numerical techniques to price American options when the underlying follows a bivariate process. The first technique exploits the semi-martingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte Carlo method. The second technique exploits recent results in the efficient pricing of American options under constant volatility. Extensive numerical evaluations show these methods yield very accurate prices in a computationally efficient manner with the latter significantly faster than the former. However, the flexibility of the first method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.
Author: Jean-Pierre Fouque
Publisher: Cambridge University Press
ISBN: 9780521791632
Category : Business & Economics
Languages : en
Pages : 222
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Book Description
This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
Author: Svetlana Boyarchenko
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.
Author: Marc Sáez i Zafra
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: An Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 149
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In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.
